On a family of data-based transformed models useful in forecasting technological substitutions

This paper examines, via real data, some well known models for technology substitution analysis. We propose a family of data-based transformed models that will include the models under examination as special cases. The basic thrust of the paper is the recognition that for technology substitution analysis, the observations are time series data and hence are not independent. Also, the functional form of the model should be determined by both theoretical considerations as well as the data on hand. This suggests that the traditional ordinary least squares procedure used in estimating the parameters and the resulting forecasting procedures are not adequate. The existing models examined here are Fisher–Pry, Gompertz, Weibull, and Normal. We stress the statistical aspects of the models and their relative merits in terms of predictive power. The criteria used for the purpose of comparison are the mean squared deviation and the mean absolute deviation of the predicted values compared with the actual observations.